The entanglement of purification

We introduce a measure of both quantum as well as classical correlations in a quantum state, the entanglement of purification. We show that the (regularized) entanglement of purification is equal to the entanglement cost of creating a state $\rho$ asymptotically from maximally entangled states, with negligible communication. We prove that the classical mutual information and the quantum mutual information divided by two are lower bounds for the regularized entanglement of purification. We present numerical results of the entanglement of purification for Werner states in ${\cal H}_2 \otimes {\cal H}_2$.Comment: 12 pages RevTex, 1 figure, to appear in JMP special issue on quantum information. v3 contains additional references, motivation, and a small change in the figur

Lower Bounds for Attainable Fidelity in Entanglement Purification

We derive lower bounds for the attainable fidelity of standard entanglement purification protocols when local operations and measurements are subjected to errors. We introduce an error parameter which measures the distance between the ideal completely positive map describing a purification step and the one in the presence of errors. We derive non--linear maps for a lower bound of the fidelity at each purification step in terms of this parameter.Comment: 11 page

Entanglement of Purification and Multiboundary Wormhole Geometries

We posit a geometrical description of the entanglement of purification for subregions in a holographic CFT. The bulk description naturally generalizes the two-party case and leads to interesting inequalities among multi-party entanglements of purification that can be geometrically proven from the conjecture. Further, we study the relationship between holographic entanglements of purification in locally-AdS3 spacetimes and entanglement entropies in multi-throated wormhole geometries constructed via quotienting by isometries. In particular, we derive new holographic inequalities for geometries that are locally AdS3 relating entanglements of purification for subregions and entanglement entropies in the wormhole geometries.Comment: 23 pages, 12 figures; v2 added references; v3 fixed inequality direction in Eq.(2), expanded discussion - reflects published versio

Entanglement purification of multi-mode quantum states

An iterative random procedure is considered allowing an entanglement purification of a class of multi-mode quantum states. In certain cases, a complete purification may be achieved using only a single signal state preparation. A physical implementation based on beam splitter arrays and non-linear elements is suggested. The influence of loss is analyzed in the example of a purification of entangled N-mode coherent states.Comment: 6 pages, 3 eps-figures, using revtex